The following are examples of chromatic dispersion compensation in an optical waveguide structure for which polarization dependence is not considered.
A dispersion compensator having a Bragg grating pattern on a waveguide is disclosed in Patent document 1. The dispersion compensator of Patent document 1 has a plurality of Bragg grating elements in which the period changes spatially such that chromatic dispersion is compensated in a plurality of wavelength channels, and a refractive index distribution n (z) of the Bragg grating which is formed by a plurality of elements extending in the direction of the optical axis of the waveguide shows sinusoidal changes as shown in the following formula (wherein z is the position of a point on the light propagation axis).
                              n          ⁡                      (            z            )                          =                                            n              eff                        ⁡                          (              z              )                                +                                    ∑                              i                =                1                            m                        ⁢                          Δ              ⁢                                                          ⁢                                                n                  i                                ⁡                                  (                  z                  )                                            ⁢                              sin                ⁡                                  (                                                                                    ∫                        0                        z                                            ⁢                                                                                                    2                            ⁢                            π                                                                                                              p                              i                                                        ⁡                                                          (                                                              z                                ′                                                            )                                                                                                      ⁢                                                  ⅆ                                                      z                            ′                                                                                                                +                                          ϕ                      i                                                        )                                                                                        [                  Expression          ⁢                                          ⁢          1                ]            
In a sine wave component which corresponds to the Bragg grating pattern of each wavelength channel, the pitch (local period) p, gradually changes (i.e., chirps) together with z. In FIG. 3 of Patent document 1, the pitch chirps in a direction in which it decreases in response to increases in z. In addition, an origin phase φi changes discretely in each grating element i. As in the above described formula, the Bragg grating pattern which corresponds to each channel is defined independently, and a Bragg grating pattern is formed by superimposing these patterns. In Patent document 1, a case is illustrated in which a Bragg grating pattern is formed in an optical fiber.
In Patent document 2, a chromatic dispersion compensator is described in which a Bragg grating having one period is formed on the waveguide path, and a sampling structure is formed on the waveguide path which is superimposed on this Bragg grating, so that chromatic dispersion compensation is performed in a plurality of wavelength channels. The sampling structure is formed by a pattern that has undergone phase sampling in one period which is longer than the period of the Bragg grating. Each period of the phase sampling is divided into a plurality of spatial areas in a direction along the optical axis of the waveguide, and the phase of the Bragg grating changes discontinuously at a boundary where mutually adjacent spatial areas are in contact with each other. As is shown in FIG. 1A through FIG. 1D of Patent document 2, there are no discontinuous phase changes within a single spatial area.
In Patent document 3, a two-input and two-output light dispersion equalizer is described that performs chromatic dispersion compensation. The optical dispersion equalizer has a structure as a basic component element in which two optical waveguides are coupled by a plurality of directional couplers, the optical path lengths of two waveguides in a region sandwiched by two adjacent directional couplers are mutually different, and a phase controller is provided in at least one of the two waveguides. In this document, a device is illustrated that compensates a dispersion slope using these waveguides, and an element that compensates chromatic dispersion is provided in an optical input section. Furthermore, this document also described that the number of stages formed by connecting the aforementioned basic component elements in series is increased in order to enhance the compensation effect.
In Patent document 4, a design method of an optical signal processor is described in which a structure provided with a directional coupler having an amplitude coupling ratio ranging from a positive value to a negative value on one side of two waveguides having an optical path difference is used as a basic component element, and these basic component elements are combined in a series so as to form a two-input and two-output optical circuit with no feedback (namely, no reflection). In this design technique, the structure of the optical circuit is decided by expressing the characteristics of the optical circuit using a two-row two-column unitary matrix, imparting the desired output characteristics of the cross-port, and calculating amplitude parameters of the directional coupler in which the amplitude parameters are unknown parameters of the optical circuit. An example of the design of a chromatic dispersion compensator that is based on this design method is given in the Examples.
In Patent document 5, a broadband chromatic dispersion compensator that employs a high refractive index waveguide that uses photonic crystals is described, and in which chromatic dispersion compensation is performed by a transmission type of optical waveguide structure. The sign of the chromatic dispersion can be changed.
In Patent document 6, a super periodic structure grating element or sampled grating element is described in which a waveguide which is formed on a substrate has a plurality of gratings, and only wavelength light of a constant FSR is output as reflection light. In the super periodic structure grating element or sampled grating element of Patent document 6, the gratings are formed in a perpendicular direction relative to the substrate with the width of the waveguide being changed periodically. In this plurality of gratings, gratings closer to input/output end surfaces of the waveguide have smaller differences in the width of the periodically changing waveguide, and gratings closer to the center between the input/output end surfaces of the waveguide have larger differences in the width of the periodically changing waveguide
In Patent document 7, a wavelength-variable element is described which comprises a first super periodic grating in which the reflection wavelength is variable, a second super periodic grating in which the reflection wavelength is variable and that has the same center wavelength as the first super periodic grating, and a ¼ period shifting structure that connects the first and second super periodic gratings together in a state in which these gratings are offset from each other by ¼ the grating period which corresponds to the center wavelength.
In Non-patent document 1, an actual fiber Bragg grating chromatic dispersion compensator is prepared using a design technique similar to that of Patent document 2, and the result of this is described. Firstly, a Bragg grating pattern of a single channel in a center wavelength is designed using the information in Non-patent document 2. The grating pattern is derived using an inverse scattering solution from the spectrum characteristics of the desired reflection and chromatic dispersion. However, in the fiber Bragg grating, because there are limits to the range over which the refractive index can be changed in order to manufacture a grating pattern, an operation in which the aforementioned spectrum characteristics are apodized by applying an inverse Fourier transform is also carried out so that these limits are not exceeded. As a result of this, a pattern is obtained in which the pitch of the Bragg grating changes continuously together with the position. Thereafter, Bragg grating patterns are designed using phase sampling for a plurality of channels. In a fiber Bragg grating, because there are limits on the range of refractive index change, phase sampling is effective.
In Non-patent document 2, an algorithm of a solution for the problem of inverse scattering which is based on layer peeling solution is described, and an example of the analysis of a chromatic dispersion compensator using a fiber Bragg grating is illustrated.
In Non-patent document 3, a chromatic dispersion compensator that is based on a chirped Bragg grating waveguide on a substrate is described. In this chromatic dispersion compensator, a rectangular optical waveguide core is formed by silver ion exchange on a silica glass substrate, and a Bragg grating pattern is formed in silica cladding on a top portion of the core. Because the grating pitch is gradually changed, the propagation axis of the core of the optical waveguide is bent. Laser light pulses having a wavelength of 800 nm are incident to the waveguide so that 58 ps/nm is obtained for an optical waveguide having a 7 mm grating length. Using a grating having a length of 50 mm, it is possible to perform chromatic dispersion compensation for an optical fiber equivalent to 50 km at a wavelength of 1550 nm.    [Patent document 1] U.S. Pat. No. 6,865,319    [Patent document 2] U.S. Pat. No. 6,707,967    [Patent document 3] Japanese Patent No. 3262312    [Patent document 4] Japanese Patent No. 3415267    [Patent document 5] Japanese Patent No. 3917170    [Patent document 6] Japanese Unexamined Patent Application, First Publication No. 2004-126172    [Patent document 7] Japanese Unexamined Patent Application, First Publication No. H9-129958    [Non-patent document 1] “Phase-Only Sampled Fiber Bragg Gratings for High-Channel-Count Chromatic Dispersion Compensation” H. Li, Y. Sheng, Y. Li and J. E. Rothenberg, Journal of Lightwave Technology, Vol. 21, No. 9, September 2003, pp. 2074-2083    [Non-patent document 2] “An Efficient Inverse Scattering Algorithm for the Design of Nonuniform Fiber Bragg Gratings” R. Feced, M. N. Zervas and M. A. Muriel, IEEE Journal of Quantum Electronics, Vol. 35, No. 8, 1999, pp. 1105-1115    [Non-patent document 3] “Integrated-Optic Dispersion Compensator that uses Chirped Gratings” C. J. Brooks, G. L. Vossler and K. A. Winick, Optics Letters, Vol. 20, No. 4, 1995, pp. 368-370